smoothing away | smoothing out

Graph smoothing, also known as smoothing away or smoothing out, is the process of replacing edges e' = v_i v_j and e'' = v_j v_k incident at a vertex v_j of vertex degree 2 by a single new edge e = v_i v_k and removing the vertex v_j. A tree which is smoothed until no vertices of degree two remain is known as a series-reduced tree. In general, a graph simple unlabeled graph whose connectivity is considered purely on the basis of topological equivalence (i.e., up to smoothing and subdivision) is known as a topological graph.

graph subdivision | homeomorphic graphs | series-reduced tree | topological graph